APPLICATION PROBLEMS ON COEFFICIENT OF VARIATION

Coefficient of variation of a data is obtained by dividing the standard deviation by the arithmetic mean. It is usually expressed in terms of percentage.

This concept is suggested by one of the most prominent Statistician Karl Pearson.

Formula to calculate coefficient of variation from mean and standard deviation is  

=  (σ/x̄) ⋅ 100%

Here σ is the standard deviation and x̄ is the mean. 

Formula to find standard deviation σ is

Formula to find arithmetic mean x̄ is

x̄  =  ∑x/n

Note :

The data with lesser coefficient of variation is more consistent or stable than the other data.

Problem 1 :

Two marks scored by two students A, B in a class are given below.

A          58          51          60          65          66

B          56          87          88          46          43

who is more consistent ?

Solution :

To check who is more consistent, let us find coefficient of variation for both A and B.

Student A :

x̄  =  (Σ x/n)

x̄  =  (58+51+60+65+66)/5

=  300/5

=  60

Σx  =  300 and Σd²  =  146

Student B :

x̄  =  (Σ x/n)

x̄  =  (56+87+88+46+43)/5

=  320/5

=  64

Σx  =  320 and Σd²  =  1934

Coefficient of variation of student A is less than student B.

So, student A is more consistent than student B.

Problem 2 :

The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, Science and Social Science are given below

Which of the three subjects shows highest variation and which shows lowest variation in marks?

Solution :

The highest variation is in the subject Science and lowest variation is in the subject Social science.

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